Question

Suppose that you put $3,000 per year in a Roth IRA (Individual Retirement Account) at the end of each year. You plan to leave these contributions and any interest and dividends earned in the account (and will reinvest in the bonds and stocks that you hold in this IRA). Suppose that your investments earn 6.6% per year, compounded annually. What will your Roth account balance be at the end of 36 years? Do not round at intermediate steps in your calculation. Round your final answer to the nearest dollar. Do not type the $ symbol.

Answer 1

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$            3,000.00
Int Rate	6.600%
Periods	36

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 3000 * [ [ ( 1 + 0.066 ) ^ 36 ] - 1 ] / 0.066
= $ 3000 * [ [ ( 1.066 ) ^ 36 ] - 1 ] / 0.066
= $ 3000 * [ [9.983] - 1 ] / 0.066
= $ 3000 * [8.983] /0.066
= $ 408316.4
Amount in Account after 36 Years is $ 408316.40